That's just one example of people who are screwed up with their idea of what race means. Just because Nazis and skinheads have a twisted view of what race means doesn't mean it has to be offensive. That's almost like thinking all postal workers kill people because one went "postal" once.
You're mistaking race for meaning species. Of course it's wrong to look at people who are different as being a different species. Here's one of Webster's definitions of race:
3. c : a category of humankind that shares certain distinctive physical traits
Youve just proved my point for me, thanks. Heritage is cultural. Race is physical. Nazis and skinheads are proud only because they are white. Other people are proud not because of the physical features of their people, but because of other cultural reasons. This is why race is such a ridiculous word.